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9. In each case, 1) show that M is a surface, and sketch its general shape when a = 3, b = 2, c = 1; (ii) show that x is a parametrization in M and describe what part of M it covers. (a) Ellipsoid. M: *+L. - 1, +- a?' b X(4, v) = (a cos u cos v, bcos u sin v, c sin u) on D: –n12 < u < #12. (b) Hyperboloid of one sheet (Fig. 4.21). x y 2 M: a - = 1, x(u, v) = (a cosh ucos v, b cosh u sin v, c sinh u) on R?.

9. In each case, 1) show that M is a surface, and sketch its general shape when a = 3, b = 2, c = 1; (ii) show that x is a parametrization in M and describe what part of M it covers. (a) Ellipsoid. M: *+L. - 1, +- a?' b X(4, v) = (a cos u cos v, bcos u sin v, c sin u) on D: –n12 < u < #12. (b) Hyperboloid of one sheet (Fig. 4.21). x y 2 M: a - = 1, x(u, v) = (a cosh ucos v, b cosh u sin v, c sinh u) on R?.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. In each case, 1) show that M is a surface, and sketch its general shape when a = 3, b = 2, c = 1; (ii) show that x is a parametrization in M and describe what part of M it covers. (a) Ellipsoid. M: *+L. - 1, +- a?' b X(4, v) = (a cos u cos v, bcos u sin v, c sin u) on D: –n12 < u < #12. (b) Hyperboloid of one sheet (Fig. 4.21). x y 2 M: a - = 1, x(u, v) = (a cosh ucos v, b cosh u sin v, c sinh u) on R?.
Transcribed Image Text:9. In each case, 1) show that M is a surface, and sketch its general shape when a = 3, b = 2, c = 1; (ii) show that x is a parametrization in M and describe what part of M it covers. (a) Ellipsoid. M: *+L. - 1, +- a?' b X(4, v) = (a cos u cos v, bcos u sin v, c sin u) on D: –n12 < u < #12. (b) Hyperboloid of one sheet (Fig. 4.21). x y 2 M: a - = 1, x(u, v) = (a cosh ucos v, b cosh u sin v, c sinh u) on R?.
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